Robyn Williams: Today's talk gives an unanswerable
reason why girls shouldn't do mathematics. At least not in the 5th Century
AD. It's an extraordinary story and here to tell it is Maths Lecturer from
Monash, Dr Michael Deakin.

Dr Deakin: Imagine a time when the world's
greatest living mathematician was a woman, indeed a physically beautiful
woman, and a woman who was simultaneously the world's leading astronomer.

And imagine that she conducted her life and her professional
work in a city as turbulent and troubled as Ayodhya or Amritsar, Belfast
or Beirut is today.

And imagine such a female mathematician achieving fame
not only in her specialist field, but also as a philosopher and religious
thinker, who attracted a large popular following.

And imagine her as a virgin martyr killed, not for her
Christianity, but by Christians because she was not one of them.

And imagine that the guilt of her death was widely whispered
to lie at the door of one of Christianity's most honoured and significant
saints.

Would we not expect to have heard of all this? Would it
not be shouted from the rooftops? Would it not be possible to walk into
any bookstore and buy a biography of this woman? Would not her life be
common knowledge?

You would think so, but such is not the case. And that
is the reason for this talk.

For Hypatia of Alexandria was indeed, at the time she
was killed by Christian fanatics, the world's foremost mathematician and
astronomer and also a leading neoplatonist philosopher. Physically beautiful,
devotedly celibate, she was the revered teacher of a man (Synesius of Cyrene)
who, after his conversion to Christianity, helped formulate the Christian
doctrine of the Trinity, using neoplatonist principles learned at her feet.

And yes, the shadow of guilt over her lynch-murder still
clouds the memory of St Cyril of Alexandria, Doctor of the Universal Church,
and in particular, Doctor of the Incarnation.

Hypatia is not quite the first woman mathematician of
whom we know. (There are at least two earlier claimants to that title.)
She is, however, the first of whom we have reasonably detailed and reliable
information. She was also the most eminent female mathematician of ancient
times - until the 18th century quite unmatched, and still the only woman
of whom it can be claimed that she was absolutely pre-eminent in the mathematical
world of her day.

I have devoted about six years to the task of finding
out about her, what it was she did, separating fact from fiction, chasing
up obscure works in which her life is discussed, trying to get a feel for
the mathematics of her era and seeking to understand where she fitted into
the intellectual life of her time.

The task is made more difficult by the fact that many
legends have come to surround her, and much of what is popularly available
is sourced to fancy or to fiction rather than to properly based historical
record.

Reliable accounts must all derive from the primary sources
that have come down to us. I have collected all these, and in English translation,
they run in total to some 14 typed pages. They include Christian writings,
"pagan" histories and "heretical" documents.

But perhaps a little background first. We now believe
that Hypatia was born in the middle years of the fourth century of the
Christian era. Around 350 say. Her home-town was Alexandria, in Egypt,
nowadays an Arab state, but in those days Greek. Her father was Theon of
Alexandria, also a mathematician, best remembered today as the source of
our text of Euclid's Elements, but also a major commentator of the work
of Ptolemy, the astronomer whose account of the solar system reigned supreme
until supplanted by Copernicus in relatively recent times.

Theon had in fact succeeded Euclid (but some 600+ years
later) as professor mathematics in what, using modern terminology, we might
describe as "The University of Alexandria". (It is, to be technical, commonly
known as "The Museum", but this gives modern eyes and ears quite the wrong
impression.) In all likelihood, Euclid was the first and Theon the last
of these professors of mathematics. We know of no scholar associated with
"The Museum" after Theon.

Theon himself was his daughter's teacher, and later the
two collaborated on an astronomical table. We aren't entirely sure quite
what this was or quite what the nature of the collaboration. However, an
early list of her publications gives this along with two other mathematical
works. These were commentaries (probably student texts) based on the work
of earlier mathematicians. One of these was a book on algebra, the other
in geometry. Sadly very little of this survives, although there have been
some attempts to reconstruct it.

We may also accept the many endorsements of her effectiveness,
indeed charisma, as a teacher of mathematics.

Hypatia was however not only a mathematician, but also
a notable philosopher and religious thinker. Her thought was neoplatonist,
and although there is some dispute about detail, we can get a feel for
its general outline. Neoplatonic thought contained a strand that is strongly
mathematical and which indeed makes mathematics a profoundly sacred pursuit.
The underlying ideas go something like this.

Quite early on in life, we learn to abstract from individual
instances and so reach a general idea of concept. Thus from our experience
of observing pairs of objects (socks, gloves, parents, whatever), we come
to form a notion of the number 2. Once we have done this, 2 becomes quite
real for us; 2 exists, although not of course in the same straightforward
way that the socks, the gloves, the parents, etc. do. This is an example
of what is called a platonic ideal.

Here, from a much later work, a 20th century work, is
an instance of how such ideals function. "... the exact sciences [are not]
based on an accumulation of statistics. In order to teach the young that
four plus three makes seven, you do not add four cakes plus three cakes
nor four bishops plus three bishops nor four cooperatives plus three cooperatives...
. Once the principle has been intuited, the youthful mathematician grasps
that four plus three invariably make seven and he does not have to prove
it over and over again with chocolates, man-eating tigers, oysters or telescopes.

The platonic ideal is thus seen as more real, more meaningful,
deeper, than the mere instances by which we are led to infer it.

These are of course other, non-mathematical, examples
of platonic ideals: truth, beauty, goodness and suchlike. We use them every
day. But perhaps the mathematical example is the clearest. Plato himself
held it in high regard, and I think we can safely say that Hypatia herself
did also.

But now suppose that we perform a further act of abstraction.
Just as the ideal is the profound reality and the exemplars merely its
manifestation, so, beyond the ideals, is an even deeper reality: the idea
of ideas, called the One. For neoplatonists, the One was not at all unlike
the Judaeo-Christian God, and indeed much Christian theology is today permeated
with neoplatonist language and thought.

One reason we know that Hypatia's philosophy gave a central
place to mathematics is that her reliance on mathematics is the source
of one of the few critical comments on her that have come down from antiquity.
the philosopher Damascius compared her unfavourably with his own idol and
mentor, Isidorus: "Isidorus," he wrote, "greatly outshone Hypatia, not
just because he was a man and she a woman, but in the way a genuine philosopher
will over a mere geometer."

Women and mathematicians alike will warm to the gloss
put on this by one modern scholar: "It means in plain language that Isidorus
knew nothing of mathematics."

However, it was not a good time to be a mathematician.
Nor a neoplatonist. By the late fourth century the Roman empire was divided
and beset, officially Christian, but holding within its sway various others:
Jews, heretical sects, diverse schools of neoplatonists and other assorted
"pagans" - and all of them at one another's throats. Alexandria in particular
was seething with intercommunal rivalry and sectarian bitterness. In either
391 or 392, the Christian archbishop, Theophilus, obtained imperial permission
to raze to the ground the temple of Serapis, the particular deity of many
Alexandrian pagans. After a series of bloody battles, he succeeded in this
aim and set out to establish on the site a church dedicated to St John
the Baptist, of whose body he had custody of some alleged relics. One theory
has it that this action also and finally put paid to the Museum and its
once glorious library.

In such a climate, mathematicians came to have a bad name,
and it's worth taking a little time to see why this should be so. The ptolemaic
system of the universe (despite its later overthrow by the copernican)
was one of the world's earliest and still greatest scientific achievements.
By its use, the positions of the planets could be foretold, and even more
tellingly, eclipses could be predicted with great accuracy.

Then as now, the business of science was, in large measure,
the quest to foretell the future. But for ordinary people in the street,
the future that most interested them was not so much the state of the heavens,
as their own immediate future. Into this void came astrology. The sun and
the moon ruled the calendar and the seasons, or even more spectacularly,
gave rise to eclipses. The other variable heavenly bodies, the planets,
it was thought, likewise had effects. They presided over the detail of
our daily lives. (Some people still believe this.)

And so there arose numerous charlatans: astrologers and
numerologists in today's terminology. The bad currency drove out the good.
Reputable astronomers and geometers like Theon and Hypatia got confused
in the popular and in the ecclesiastical mind with these fly-by-nights.
All were lumped together as "mathematicians".

The council of Laodicea in the mid-4th century outlawed
"divination" and forbade priests to practise mathematics; at about the
same time. the emperor Constantius promulgated a law that "No one may consult
a soothsayer or a mathematician". Apparently not everyone complied. Hypatia's
contemporary, St Augustine of Hippo tried a neat bit of casuistry before
disillusionment set in: "Those imposters," he wrote, "whom they call 'Mathematicians'
I consulted without scruple; because they seemed to use no sacrifice nor
to pray to any spirit for their divinations" which art, however, Christian
piety consistently rejects and condemns."

This is the background to Hypatia's murder. In the year
412 Archbishop Theophilus died and was succeeded by his nephew Cyril. Although
Theophilus had razed the temple of Serapis, he had never, in over 30 years,
moved against Hypatia. In part this may very well have been a result of
his friendship with Hypatia's influential and adoring pupil, Synesius of
Cyrene. Synesius himself died in 413 or thereabouts, and so Hypatia was
suddenly left without her powerful protectors.

Cyril, making use of a 500-strong private militia, began
to exert his authority in the temporal as well as in the spiritual sphere,
and thus he came into conflict with the civil governor, Orestes, in the
course of a series of increasingly violent confrontations between the various
factions in the city. In 415 and as the violence escalated, his powerful
militia made a direct assassination attempt on Orestes himself. However
this failed and the governor was able to apprehend one of the ringleaders,
whom he tortured so severely that the man died. Cyril was furious and,
managing to get hold of the body, pronounced over it a ceremony of canonisation,
enrolling the would-be assassin in the calendar of the saints (where incidentally
he remained until this century).

However the militia were not about to leave matters there.
Hypatia was close to Orestes and there was a rumour that it was Hypatia's
influence that prevented the Christian Orestes from accepting Cyril's spiritual
direction and so becoming reconciled with his rival. Moreover she was seen
as one "devoted at all times to magic, astrolabes and instruments of music,
[who] beguiled many people through her satanic wiles, and the governor
... through her magic." That this was not in fact true is beside the point;
it was believed and was bruited abroad.

So somewhat later, as Hypatia was returning home, she
was set upon, torn from her carriage and dragged into a church, where she
was stripped naked and battered to death with roofing tiles, "and while
she was still feebly twitching they beat her eyes out". They then orgiastically
tore her body limb from limb, took her mangled remains out from the church,
and burned them.

The question of Cyril's complicity in this affair has
long been hotly debated. Assessments are normally made along "party lines".
Roman Catholic commentators normally stoutly defend him; anti-clericals
gleefully denounce the man. Perhaps the closest we find to a balanced view
is that of the Anglican historian Canon Bright, who wrote: "Cyril was no
party to this hideous deed, but it was the work of men whose passions he
had originally called out. Had there been no [earlier such episodes], there
would doubtless have been no murder of Hypatia."

But even this moderate line may perhaps be queried. Cyril
is especially venerated by the Coptic church, and last century, among their
archives, an Ethiopic translation of an old Greek text was discovered.
So if more needs to be said, let us take it from the mouth of Cyril's most
vigorous defender, the Coptic bishop John of Nikiu: "[After Hypatia's death]
all the people surrounded the patriach Cyril and named him 'the new Theophilus';
for he had destroyed the last remains of idolatry in the city."

With this as the defence, what further need have we of
witnesses?

Robyn Williams: What need indeed. That was Michael
Deakin who lectures in mathematics at Monash University in Melbourne. And
Hypatia also featured in Margaret Wetheim's excellent book "Pythagoras's
Trousers". Next week Okham's Razor comes from Canberra where Colin Groves
has been thinking all about Okham's Razor, and Charles Darwin.

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